Dafny is an imperative compiled language that supports formal specification through preconditions, postconditions, loop invariants.
I found out about it from The Great Theorem Prover Showdown, while reading Hacker News one day.
It only seems to target C#, but can automatically prove properties about functions nevertheless.
I finished Dafny Tutorial and it was pretty straight-forward. The tutorial should be easy to follow for anyone with basic knowledge with the C programming language (and mathematical logic). The examples for the Dafny tutorial can be ran from the browser so you do not have to install it locally to go through it.
The reason why I like this programming language is because it seems much simpler than e.g. Coq or Idris that are based on dependent types / Calculus of Constructions (however, note that it still shares some stuff such as algebraic data types, or inductive types).
The tutorial starts with functions, pre-post conditions and assertions, and then proceeds with loop invariants. It proves basic properties for abs/max, etc.
For example, abs takes an integer and produces an integer greater than or equal to zero. Here’s the proof for that:
method Abs(x: int) returns (y: int)
ensures 0 <= y
y := 0;
ensures we set the post-conditions (alternatively,
requires is for pre-conditions). Pretty simple and neat, right? 🙂
Like pre- and postconditions, an invariant is a property that is preserved for each execution of the loop. Here’s an example for an invariant:
method m(n: nat)
var i := 0;
while i < n
invariant 0 <= i
i := i + 1;
However if you go through the tutorial you will see by the exercises that the challenge in picking a good loop invariant is finding one that is preserved with each loop execution, but also one that lets you prove what you need.
Finally, example for quantifiers:
assert forall k :: k < k + 1;
The tutorial takes only a couple of hours to finish, and for anyone interested in programming languages like this I highly recommend you go through it 🙂
The conclusion paragraph of the tutorial states it well:
Even if you do not use Dafny regularly, the idea of writing down exactly what it is that the code does is a precise way, and using this to prove code correct is a useful skill. Invariants, pre- and post conditions, and annotations are useful in debugging code, and also as documentation for future developers. When modifying or adding to a codebase, they confirm that the guarantees of existing code are not broken. They also ensure that APIs are used correctly, by formalizing behavior and requirements and enforcing correct usage. Reasoning from invariants, considering pre- and postconditions, and writing assertions to check assumptions are all general computer science skills that will benefit you no matter what language you work in.
For all the tutorial exercises, you can check out my Dafny Git repository.